Study of Interaction Patterns in Primary School Children Network
Utsab Shrestha
May 25,2020
Introduction
Human interactions and human behaviors has been a fascinating and challenging subject of study in recent times. Social network companies, consumer markets, medical industries have been trying to study human behavior to predict the consumer needs, recommend goods, optimize marketing strategies, or in case of medical industry diagnose and study disease patterns. Child psychology and child interaction behavior is very different from an adult behavior. Study of children interaction pattern is very important to understand and improve the development of children. These studies have been used to understand the development in children as well as spreading of highly communicable disease like influenza, hepatitis and measles. Children are prone to these diseases and the pattern study of interaction of children helps to find the propagation and evaluation of the control measures of these diseases. Through this study, we want to find how age, gender, grade affect the interaction pattern in children.
Data
Data for this project was obtained from the Socio patterns website (sociopatterns.org). The dataset had two networks, one for each day, of face-to-face interaction between students and teachers. These interactions were collected from a French school in 2009 using radio frequency identification devices that recognizes an interaction by proximity sensors. The students involved in the data are ages 6 to 12 attending grades 1 to 5. There were 232 children and 10 teachers who were involved in 77,602 contacts amongst each other in course of two days. There were 10 classes, grades 1 to 5 with section A and B, and in each grade, there were around 25 students. In average, each child had around 165 interactions and spent an average of 176 minutes in interaction per day. The gender and grade were provided for the children and also the count and duration of interactions were provided. For a contact to occur between two individuals, they must be in certain proximity for at least 20 seconds. A packet of information is sent after every 20 second. A contact is broken once they are further than the defined proximity and if they come in contact again new contact is added and time is added to previous duration.
Analysis
Analysis for this project was focused on finding patterns of interaction by grades and gender to study if the students show homophile behavior. Do children of opposite sex interact as much as same sex? Which grades/age children are more social? How popular are the most popular student? In following analysis we will be trying to answer these quesitons.
Data Exploration
The files from the data source website were in GEXF gephi format, one file for each day. I loaded the files in gephi and explored different layouts to visualize the network data.
Using the gephi community detection, there were 8 communities detected for both days with modularity of 0.75. The algorithm performs well on separating communities by grades. Same grade students form a community. This measure shows how well the network can decomposed into modular communities. Grades 2A and 2B are in same community, grade 5A and grade 5B are in same communities while Grades 1A and 1B, 3A and 3B, and 4A and 4B form separate communities. This also shows sign of homophile behavior since there is high interaction between same grade students which resulted in same grade students being in same community.
Over the course of two days, grade 1B had the most interactions. Comparing to the other section, the same grade (1A) students had half the number of contacts. Teachers seem to have the least contacts and among the classes grade 4B had the lowest number of contacts.
The average weighted degree was 10 and maximum was 23. This means in average a student interacted with 10 individual and the student who had the most interactions connected with 23 other students in the given day.
In the histogram, we see the distribution of weighted degree by gender. For both male and female students, the histogram looks normally distributed with most students towards the middle of the chart. We can say, the chart is a bit skewed to the right since there are few students with high degree.
When comparing boys versus girls, looks like boys are more interactive. Girls have degree 10 as the highest count which means degree 10 is the most common amongst the girls. Whereas for boys degree 14 is the most common degree. Also the person with highest degree(23) is a boy.
In the above graph, the nodes are sized by weighted degree and the label size by node size. The color of the nodes are partitioned by the grades. There are grades 1 to 5 with 2 sections for each grade. Teacher nodes are colored red.
In this network, students in same grade are grouped together because they are more likely to form their own committee with most interaction happening with students in same grade. Grade 1B clearly pop out with most students in the class with higher weighted degree. Grade 1B students are highly interactive with larger nodes. Furthermore,grades 2B, 4A and 3B have one student each with relatively big nodes. These individual students are likely to be the most social student in those classes. In contrast, grades 4B and 2A don’t seem to have high degree nodes. Few dark edges are visible explaning they might have had interaction between fewer students but those interactions were significant ( longer or multiple interaction between same students).
Interestingly, teacher do not show high weighted degree. One teacher in the middle of 1B student nodes look to be more interactive than others.
There is a strong correlation between degree and pagerank. This means important nodes are high degree nodes. Another interesting insight is betweenness centrality and degree centrality are not strongly correlated. This means high degree nodes are not the connections for most interactions. This proves that the most interactive student may not be the fastest connection between two students.
In addition, there seem to be no correlation between eigenvector and betweenness centrality. With means most influencing students in this network are not the in-between connections for most interaction. There are many students and many interactions happening so even the most influencing students would not necessarily be the connections for other students interactions.
To look at the most influencing node we check the eigenvector centrality measure. High degree nodes do not necessarily the most important nodes. It uses adjacency matrix of the graph to calculate the eigenvalues.
The graph above shows the top three highest degree nodes. These are nodes 1697, 1890 and 1688. They are from Grades 1B and 2B. They have weighted degree of 23 and 22. The color of the nodes are based on the male and female gender and the red node is the highest degree node.
The students from smaller grades have higher degree interaction and are more influencing. As the kids get older they seem to have smaller friend circle and less interactions between them.
Network properties
## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] 10## [1] 9Degree Boxplot by Grade
### Giant Components
## [1] 234## IGRAPH UN-- 234 1148 --
## + attr: name (v/c), Label (v/n), timeset (v/l), X0 (v/c), X1
## | (v/c), Age (v/n), Grade (v/c), Type (e/c), Id (e/n), Label
## | (e/l), timeset (e/l), Weight (e/n), X2 (e/n), X3 (e/n),
## | Calc.Weight (e/n)## [1] 235## IGRAPH UN-- 235 1328 --
## + attr: name (v/c), Label (v/n), timeset (v/l), X0 (v/c), X1
## | (v/c), Age (v/n), Grade (v/c), Type (e/c), Id (e/n), Label
## | (e/l), timeset (e/l), Weight (e/n), X2 (e/n), X3 (e/n),
## | Calc.Weight (e/n)Centrality Measures Corr Plot
### Betweeness and Closeness Distributon 
### ERGM Models
Model 1 for Day 1
simple model no mcmc stored
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3))
##
## Iterations: 6 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -3.29971 0.09937 0 < 1e-04 ***
## mix.X1.F.F 0.30291 0.11672 0 0.00946 **
## mix.X1.F.M -0.08278 0.11159 0 0.45822
## mix.X1.M.M 0.51647 0.11317 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 9448 on 27257 degrees of freedom
##
## AIC: 9456 BIC: 9489 (Smaller is better.)
### Model 2 added Age difference and MCMC burnin
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -0.85584 0.11355 0 <1e-04 ***
## mix.X1.F.F -0.98609 0.12690 0 <1e-04 ***
## mix.X1.F.M -1.38049 0.12180 0 <1e-04 ***
## mix.X1.M.M -0.74723 0.12358 0 <1e-04 ***
## absdiff.Age -1.13837 0.04038 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 8048 on 27256 degrees of freedom
##
## AIC: 8058 BIC: 8099 (Smaller is better.)Model 3
added Degree 1
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + degree(2:4) +
## degree(8:9) + absdiff("Age")
##
## Iterations: 4 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -0.79269 0.12165 0 < 1e-04 ***
## mix.X1.F.F -0.92745 0.12788 0 < 1e-04 ***
## mix.X1.F.M -1.35689 0.12719 0 < 1e-04 ***
## mix.X1.M.M -0.75709 0.12808 0 < 1e-04 ***
## degree2 2.11227 0.43478 0 < 1e-04 ***
## degree3 1.59528 0.35976 0 < 1e-04 ***
## degree4 1.27480 0.30049 0 < 1e-04 ***
## degree8 -0.86100 0.33498 0 0.01017 *
## degree9 -0.88450 0.31153 0 0.00453 **
## absdiff.Age -1.14815 0.04086 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 7984 on 27251 degrees of freedom
##
## AIC: 8004 BIC: 8086 (Smaller is better.)
### Model 4 updated degree(2:4) based on GOF from Model 3 and added gwesp
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + degree(2:4) +
## degree(8:9) + absdiff("Age") + gwesp(cutoff = 7)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -2.57449 0.14157 1 <1e-04 ***
## mix.X1.F.F -0.61957 0.09787 2 <1e-04 ***
## mix.X1.F.M -1.03755 0.10462 2 <1e-04 ***
## mix.X1.M.M -0.56446 0.09720 2 <1e-04 ***
## degree2 0.68043 0.40375 0 0.0919 .
## degree3 0.78350 0.43555 0 0.0721 .
## degree4 0.48634 0.45145 0 0.2814
## degree8 -0.74868 0.62571 0 0.2315
## degree9 -0.81530 0.55616 0 0.1427
## absdiff.Age -0.72378 0.02590 1 <1e-04 ***
## gwesp 0.51594 0.02432 0 <1e-04 ***
## gwesp.decay 1.31566 0.03398 1 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 7579 on 27249 degrees of freedom
##
## AIC: 7603 BIC: 7702 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 50000:5165000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 1993.991 85.432 2.66975 16.54264
## mix.X1.F.F 522.465 33.063 1.03323 4.61356
## mix.X1.F.M 709.263 42.547 1.32959 6.85926
## mix.X1.M.M 603.961 37.210 1.16280 4.44671
## degree2 4.781 2.187 0.06836 0.14928
## degree3 5.129 2.587 0.08083 0.28338
## degree4 4.176 2.386 0.07458 0.32020
## degree8 2.431 1.569 0.04904 0.07042
## degree9 2.754 1.655 0.05172 0.05783
## absdiff.Age 1240.912 76.248 2.38274 6.86244
## gwesp 4463.521 268.355 8.38610 49.36679
## gwesp.decay -2884.815 130.673 4.08354 24.39587
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 1813.6 1942.8 2002 2053 2140.0
## mix.X1.F.F 458.0 499.0 524 546 584.4
## mix.X1.F.M 625.6 680.8 709 740 787.4
## mix.X1.M.M 532.0 580.0 604 631 671.4
## degree2 1.0 3.0 5 6 9.0
## degree3 1.0 3.0 5 7 11.0
## degree4 0.0 2.0 4 6 9.0
## degree8 0.0 1.0 2 3 6.0
## degree9 0.0 2.0 3 4 6.0
## absdiff.Age 1079.2 1190.0 1241 1294 1386.7
## gwesp 3879.0 4300.5 4487 4657 4921.0
## gwesp.decay -3101.4 -2979.3 -2901 -2804 -2610.1
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2
## edges 1.0000000 0.64854114 0.8473006 0.66909334 -0.34776211
## mix.X1.F.F 0.6485411 1.00000000 0.4125069 0.09486298 -0.24939066
## mix.X1.F.M 0.8473006 0.41250687 1.0000000 0.38999358 -0.30414068
## mix.X1.M.M 0.6690933 0.09486298 0.3899936 1.00000000 -0.21657916
## degree2 -0.3477621 -0.24939066 -0.3041407 -0.21657916 1.00000000
## degree3 -0.4791986 -0.33282169 -0.3939830 -0.30668792 0.11019782
## degree4 -0.5030838 -0.35440506 -0.4080000 -0.31108568 0.16934546
## degree8 -0.2700660 -0.16662641 -0.2320741 -0.18428319 0.06477757
## degree9 -0.1697598 -0.10636084 -0.1633089 -0.11039807 0.04748921
## absdiff.Age 0.8194284 0.49995212 0.6811516 0.58627193 -0.25891210
## gwesp 0.9827517 0.64829234 0.8339447 0.65144855 -0.31941027
## gwesp.decay -0.9627086 -0.61906952 -0.8130220 -0.64600436 0.37562961
## degree3 degree4 degree8 degree9 absdiff.Age
## edges -0.47919863 -0.50308376 -0.27006600 -0.16975981 0.8194284
## mix.X1.F.F -0.33282169 -0.35440506 -0.16662641 -0.10636084 0.4999521
## mix.X1.F.M -0.39398301 -0.40800002 -0.23207413 -0.16330886 0.6811516
## mix.X1.M.M -0.30668792 -0.31108568 -0.18428319 -0.11039807 0.5862719
## degree2 0.11019782 0.16934546 0.06477757 0.04748921 -0.2589121
## degree3 1.00000000 0.22482332 0.07107867 0.02340122 -0.3496623
## degree4 0.22482332 1.00000000 0.07399524 0.05081019 -0.3556496
## degree8 0.07107867 0.07399524 1.00000000 0.05703447 -0.1979823
## degree9 0.02340122 0.05081019 0.05703447 1.00000000 -0.1183437
## absdiff.Age -0.34966228 -0.35564960 -0.19798227 -0.11834366 1.0000000
## gwesp -0.44102066 -0.47915968 -0.28239490 -0.17741969 0.7699191
## gwesp.decay 0.49707056 0.51928048 0.26575648 0.16758550 -0.7969449
## gwesp gwesp.decay
## edges 0.9827517 -0.9627086
## mix.X1.F.F 0.6482923 -0.6190695
## mix.X1.F.M 0.8339447 -0.8130220
## mix.X1.M.M 0.6514485 -0.6460044
## degree2 -0.3194103 0.3756296
## degree3 -0.4410207 0.4970706
## degree4 -0.4791597 0.5192805
## degree8 -0.2823949 0.2657565
## degree9 -0.1774197 0.1675855
## absdiff.Age 0.7699191 -0.7969449
## gwesp 1.0000000 -0.9279204
## gwesp.decay -0.9279204 1.0000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.9008796 0.8422287 0.8239322 0.8410396 0.3033610 0.3913391
## Lag 10000 0.8208001 0.7345352 0.7122471 0.7410395 0.2166939 0.3048311
## Lag 15000 0.7541697 0.6563672 0.6269672 0.6585687 0.2042927 0.3007758
## Lag 20000 0.6883340 0.5968886 0.5518889 0.5831834 0.1772719 0.2663521
## Lag 25000 0.6426112 0.5315558 0.4944206 0.5321341 0.1223783 0.2651056
## degree4 degree8 degree9 absdiff.Age gwesp
## Lag 0 1.0000000 1.00000000 1.000000000 1.0000000 1.0000000
## Lag 5000 0.3854949 0.07004986 0.050475523 0.7657024 0.8839421
## Lag 10000 0.3547671 0.13405949 0.062588166 0.6057205 0.7897196
## Lag 15000 0.3339432 0.04682326 -0.020676629 0.4896142 0.7199504
## Lag 20000 0.3025383 0.06597519 0.030875139 0.3967045 0.6551354
## Lag 25000 0.3236647 0.09748826 -0.003226675 0.3314613 0.6111442
## gwesp.decay
## Lag 0 1.0000000
## Lag 5000 0.9043520
## Lag 10000 0.8361846
## Lag 15000 0.7747848
## Lag 20000 0.7190098
## Lag 25000 0.6771558
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## 0.3971 0.6746 -0.4449 0.7307 -1.4091 -1.0110
## degree4 degree8 degree9 absdiff.Age gwesp gwesp.decay
## -1.0313 -1.0327 -0.3278 0.4542 0.4160 -0.4288
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M degree2 degree3
## 0.6913113 0.4999042 0.6563927 0.4649537 0.1587952 0.3120213
## degree4 degree8 degree9 absdiff.Age gwesp gwesp.decay
## 0.3024063 0.3017263 0.7430849 0.6496927 0.6774031 0.6680948
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
### Model 6 added Degree 9, nodematch for Grade and increased burnin computation This is much better model. MCMC statistics show some autocorrelation but the joint pvalue is better.
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_1.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + nodematch("X0") +
## degree(2:4) + degree(9)
##
## Iterations: 4 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -3.68843 0.08760 0 < 1e-04 ***
## mix.X1.F.F -0.42904 0.09784 0 < 1e-04 ***
## mix.X1.F.M -1.04572 0.09695 0 < 1e-04 ***
## mix.X1.M.M -0.26522 0.09314 0 0.00441 **
## nodematch.X0 3.94314 0.07686 0 < 1e-04 ***
## degree2 4.14135 0.33006 0 < 1e-04 ***
## degree3 2.95658 0.33088 0 < 1e-04 ***
## degree4 2.23026 0.29091 0 < 1e-04 ***
## degree9 -0.84032 0.31849 0 0.00833 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 37792 on 27261 degrees of freedom
## Residual Deviance: 6099 on 27252 degrees of freedom
##
## AIC: 6117 BIC: 6191 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 1e+05:20575000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 4096
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges -13.66382 91.473 1.42927 13.80263
## mix.X1.F.F -5.46997 30.855 0.48210 3.66628
## mix.X1.F.M -6.93506 37.769 0.59014 4.99763
## mix.X1.M.M -2.09766 27.852 0.43518 2.54928
## nodematch.X0 -8.74414 63.205 0.98758 9.28293
## degree2 0.75586 5.859 0.09154 0.84932
## degree3 0.91235 5.705 0.08914 0.81774
## degree4 1.16602 6.407 0.10012 0.81451
## degree9 -0.07227 3.259 0.05092 0.06986
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges -234.6 -66.25 2 50.00 129.6
## mix.X1.F.F -72.0 -25.00 -3 17.00 49.0
## mix.X1.F.M -93.0 -29.00 -2 20.00 55.0
## mix.X1.M.M -66.0 -20.00 0 17.00 46.0
## nodematch.X0 -162.0 -45.00 1 36.25 90.0
## degree2 -7.0 -3.00 0 4.00 15.0
## degree3 -8.0 -3.00 0 4.00 15.0
## degree4 -9.0 -3.25 0 5.00 16.0
## degree9 -6.0 -2.00 0 2.00 7.0
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## edges 1.00000000 0.85775713 0.92400390 0.77151715 0.97567718
## mix.X1.F.F 0.85775713 1.00000000 0.75043524 0.47152503 0.84151366
## mix.X1.F.M 0.92400390 0.75043524 1.00000000 0.62203424 0.91914532
## mix.X1.M.M 0.77151715 0.47152503 0.62203424 1.00000000 0.75578202
## nodematch.X0 0.97567718 0.84151366 0.91914532 0.75578202 1.00000000
## degree2 -0.83441832 -0.73487368 -0.77051072 -0.60486427 -0.81447905
## degree3 -0.82723780 -0.72330528 -0.76458964 -0.61704506 -0.80854331
## degree4 -0.81875942 -0.71433137 -0.75141628 -0.62239090 -0.79804457
## degree9 0.05053908 0.07348491 0.05065768 -0.00826246 0.04504015
## degree2 degree3 degree4 degree9
## edges -0.8344183 -0.82723780 -0.8187594 0.05053908
## mix.X1.F.F -0.7348737 -0.72330528 -0.7143314 0.07348491
## mix.X1.F.M -0.7705107 -0.76458964 -0.7514163 0.05065768
## mix.X1.M.M -0.6048643 -0.61704506 -0.6223909 -0.00826246
## nodematch.X0 -0.8144790 -0.80854331 -0.7980446 0.04504015
## degree2 1.0000000 0.65407198 0.6260663 -0.13268049
## degree3 0.6540720 1.00000000 0.6033828 -0.09768586
## degree4 0.6260663 0.60338279 1.0000000 -0.09415660
## degree9 -0.1326805 -0.09768586 -0.0941566 1.00000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.9511848 0.9052019 0.8999225 0.8554150 0.9687199
## Lag 10000 0.9250263 0.8631506 0.8516169 0.7932068 0.9416796
## Lag 15000 0.9049214 0.8312281 0.8170676 0.7516522 0.9180119
## Lag 20000 0.8860790 0.8069029 0.7869850 0.7144684 0.8957487
## Lag 25000 0.8699562 0.7834487 0.7614632 0.6752455 0.8737800
## degree2 degree3 degree4 degree9
## Lag 0 1.0000000 1.0000000 1.0000000 1.00000000
## Lag 5000 0.7785616 0.7214853 0.7117399 0.05549559
## Lag 10000 0.7399260 0.7013840 0.6892196 0.07378195
## Lag 15000 0.7213618 0.6884767 0.6714934 0.04825174
## Lag 20000 0.7047914 0.6708178 0.6535243 0.02863306
## Lag 25000 0.6991061 0.6530943 0.6388633 0.03976281
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.5443 0.4658 0.6542 0.9741 0.5935
## degree2 degree3 degree4 degree9
## -0.6367 -0.4703 -0.5762 0.6156
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.5862662 0.6413416 0.5129901 0.3300264 0.5528261
## degree2 degree3 degree4 degree9
## 0.5243065 0.6381238 0.5644464 0.5381821
## Joint P-value (lower = worse): 0.9940786 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
Model 1 for Day 2
Simple model to begin with
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1") + nodematch("X0")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -6.56876 0.60448 0 < 1e-04 ***
## mix.X1.F.F 2.21000 0.60464 0 0.000258 ***
## mix.X1.F.M 1.81354 0.60285 0 0.002630 **
## mix.X1.M.M 2.56825 0.60450 0 < 1e-04 ***
## mix.X1.F.Unknown 2.61712 0.62282 0 < 1e-04 ***
## mix.X1.M.Unknown 2.62221 0.62233 0 < 1e-04 ***
## mix.X1.Unknown.Unknown NA 0.00000 0 NA
## nodematch.X0 4.08483 0.07257 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6654 on 27487 degrees of freedom
##
## AIC: 6670 BIC: 6736 (Smaller is better.)Model 2 and 3
added age difference and nodemix for gender
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.12167 0.10696 0 <1e-04 ***
## mix.X1.F.F -0.71536 0.11890 0 <1e-04 ***
## mix.X1.F.M -0.98003 0.11338 0 <1e-04 ***
## mix.X1.M.M -0.47303 0.11663 0 <1e-04 ***
## absdiff.Age -0.96642 0.03418 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 9290 on 27490 degrees of freedom
##
## AIC: 9300 BIC: 9341 (Smaller is better.)
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodemix("X1", base = c(-1, -2, -3)) + nodematch("X0") +
## absdiff("Age") + degree(2:5) + degree(8) + degree(12)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.26211 0.06646 0 <1e-04 ***
## mix.X1.F.F 0.14024 0.06037 0 0.0202 *
## mix.X1.F.M -0.13757 0.05911 0 0.0199 *
## mix.X1.M.M 0.47062 0.05744 0 <1e-04 ***
## nodematch.X0 2.97452 0.07566 1 <1e-04 ***
## absdiff.Age 0.29011 0.01011 0 <1e-04 ***
## degree2 14.61122 NA NA NA
## degree3 7.65666 NA NA NA
## degree4 4.82784 NA NA NA
## degree5 3.33014 NA NA NA
## degree8 -1.75119 NA NA NA
## degree12 0.11071 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 28109 on 27483 degrees of freedom
##
## AIC: 28133 BIC: 28232 (Smaller is better.)
## Sample statistics summary:
##
## Iterations = 1e+05:5215000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 10288 74.46 2.3269 6.071
## mix.X1.F.F 2177 35.91 1.1222 3.078
## mix.X1.F.M 3845 46.99 1.4683 3.588
## mix.X1.M.M 2501 36.98 1.1556 3.443
## nodematch.X0 1150 14.56 0.4551 1.771
## absdiff.Age 25710 200.94 6.2795 18.388
## degree2 -10 0.00 0.0000 0.000
## degree3 -8 0.00 0.0000 0.000
## degree4 -10 0.00 0.0000 0.000
## degree5 -14 0.00 0.0000 0.000
## degree8 -8 0.00 0.0000 0.000
## degree12 -9 0.00 0.0000 0.000
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 10146 10238 10289 10337 10434
## mix.X1.F.F 2105 2153 2177 2201 2249
## mix.X1.F.M 3752 3814 3844 3879 3938
## mix.X1.M.M 2430 2475 2502 2526 2576
## nodematch.X0 1124 1140 1150 1161 1181
## absdiff.Age 25325 25576 25706 25843 26117
## degree2 -10 -10 -10 -10 -10
## degree3 -8 -8 -8 -8 -8
## degree4 -10 -10 -10 -10 -10
## degree5 -14 -14 -14 -14 -14
## degree8 -8 -8 -8 -8 -8
## degree12 -9 -9 -9 -9 -9
##
##
## Sample statistics cross-correlations:
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## edges 1.0000000 0.54110445 0.63901830 0.49683419 0.12757846
## mix.X1.F.F 0.5411044 1.00000000 0.04170776 0.06302899 0.08773853
## mix.X1.F.M 0.6390183 0.04170776 1.00000000 -0.02088295 0.04121998
## mix.X1.M.M 0.4968342 0.06302899 -0.02088295 1.00000000 0.12425320
## nodematch.X0 0.1275785 0.08773853 0.04121998 0.12425320 1.00000000
## absdiff.Age 0.7620371 0.36743234 0.36642576 0.35916330 -0.11559052
## degree2 NA NA NA NA NA
## degree3 NA NA NA NA NA
## degree4 NA NA NA NA NA
## degree5 NA NA NA NA NA
## degree8 NA NA NA NA NA
## degree12 NA NA NA NA NA
## absdiff.Age degree2 degree3 degree4 degree5 degree8 degree12
## edges 0.7620371 NA NA NA NA NA NA
## mix.X1.F.F 0.3674323 NA NA NA NA NA NA
## mix.X1.F.M 0.3664258 NA NA NA NA NA NA
## mix.X1.M.M 0.3591633 NA NA NA NA NA NA
## nodematch.X0 -0.1155905 NA NA NA NA NA NA
## absdiff.Age 1.0000000 NA NA NA NA NA NA
## degree2 NA 1 NA NA NA NA NA
## degree3 NA NA 1 NA NA NA NA
## degree4 NA NA NA 1 NA NA NA
## degree5 NA NA NA NA 1 NA NA
## degree8 NA NA NA NA NA 1 NA
## degree12 NA NA NA NA NA NA 1
##
## Sample statistics auto-correlation:
## Chain 1
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.7435861 0.7651016 0.7128441 0.7973492 0.8759881
## Lag 10000 0.5630193 0.6035315 0.5284366 0.6337419 0.7704237
## Lag 15000 0.4224339 0.4605978 0.3677002 0.4961827 0.6711204
## Lag 20000 0.3164321 0.3457924 0.2691034 0.4018330 0.5953178
## Lag 25000 0.2353476 0.2733610 0.2001352 0.3189354 0.5164186
## absdiff.Age degree2 degree3 degree4 degree5 degree8 degree12
## Lag 0 1.0000000 NaN NaN NaN NaN NaN NaN
## Lag 5000 0.7909311 NaN NaN NaN NaN NaN NaN
## Lag 10000 0.6268851 NaN NaN NaN NaN NaN NaN
## Lag 15000 0.4979887 NaN NaN NaN NaN NaN NaN
## Lag 20000 0.4193958 NaN NaN NaN NaN NaN NaN
## Lag 25000 0.3498309 NaN NaN NaN NaN NaN NaN
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.8993 0.4526 0.4244 -0.1207 -0.7585
## absdiff.Age degree2 degree3 degree4 degree5
## 2.2353 NaN NaN NaN NaN
## degree8 degree12
## NaN NaN
##
## Individual P-values (lower = worse):
## edges mix.X1.F.F mix.X1.F.M mix.X1.M.M nodematch.X0
## 0.36847482 0.65086571 0.67130254 0.90392120 0.44814787
## absdiff.Age degree2 degree3 degree4 degree5
## 0.02540091 NaN NaN NaN NaN
## degree8 degree12
## NaN NaN
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).Model 4
added Nodematch for Grade and Degrees based on GOF and also increased computational power
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0",
## diff = T) + absdiff("Age")
##
## Iterations: 6 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -5.03047 0.10436 0 < 1e-04 ***
## nodematch.X1.F 0.28886 0.08749 0 0.000963 ***
## nodematch.X1.M 0.74920 0.08435 0 < 1e-04 ***
## nodematch.X1.Unknown 0.30588 0.75447 0 0.685168
## nodematch.X0.1A 3.87557 0.16913 0 < 1e-04 ***
## nodematch.X0.1B 4.91508 0.14924 0 < 1e-04 ***
## nodematch.X0.2A 5.08792 0.15856 0 < 1e-04 ***
## nodematch.X0.2B 4.18506 0.14944 0 < 1e-04 ***
## nodematch.X0.3A 4.48412 0.15777 0 < 1e-04 ***
## nodematch.X0.3B 5.27094 0.17080 0 < 1e-04 ***
## nodematch.X0.4A 3.78439 0.18224 0 < 1e-04 ***
## nodematch.X0.4B 3.20159 0.21147 0 < 1e-04 ***
## nodematch.X0.5A 4.79063 0.16781 0 < 1e-04 ***
## nodematch.X0.5B 4.09425 0.16255 0 < 1e-04 ***
## nodematch.X0.Teachers 1.16924 1.27047 0 0.357412
## absdiff.Age 0.16816 0.02633 0 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6465 on 27479 degrees of freedom
##
## AIC: 6497 BIC: 6629 (Smaller is better.)
### Model 5 AIC and BIC are still not looking good. P-values are not significant. GOF is not performing well
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age")
##
## Iterations: 7 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -5.02913 0.10354 0 <1e-04 ***
## nodematch.X1.F 0.33879 0.08444 0 <1e-04 ***
## nodematch.X1.M 0.69893 0.08213 0 <1e-04 ***
## nodematch.X1.Unknown -1.90835 0.60111 0 0.0015 **
## nodematch.X0 4.42033 0.10093 0 <1e-04 ***
## absdiff.Age 0.17097 0.02618 0 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 6654 on 27489 degrees of freedom
##
## AIC: 6666 BIC: 6715 (Smaller is better.)
### Model 6 MCMC statistics have high correlations, and joint p-value is also 0.
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age") + degree(1:5)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges -1.44779 0.02836 0 <1e-04 ***
## nodematch.X1.F 0.32826 0.03589 0 <1e-04 ***
## nodematch.X1.M 0.46388 0.03680 0 <1e-04 ***
## nodematch.X1.Unknown -0.01960 0.24919 1 0.937
## nodematch.X0 2.87234 0.05881 1 <1e-04 ***
## absdiff.Age 0.20200 0.00702 0 <1e-04 ***
## degree1 15.87292 NA NA NA
## degree2 17.96196 NA NA NA
## degree3 12.06530 NA NA NA
## degree4 9.02377 NA NA NA
## degree5 4.53998 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 21444 on 27484 degrees of freedom
##
## AIC: 21466 BIC: 21556 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 1e+05:5215000
## Thinning interval = 5000
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 8671.02 71.864 2.2458 5.967
## nodematch.X1.F 1989.81 34.564 1.0801 2.809
## nodematch.X1.M 2035.56 34.482 1.0776 2.926
## nodematch.X1.Unknown 53.56 4.058 0.1268 0.412
## nodematch.X0 1082.63 18.173 0.5679 2.341
## absdiff.Age 20157.12 224.372 7.0116 21.714
## degree1 -6.00 0.000 0.0000 0.000
## degree2 -10.00 0.000 0.0000 0.000
## degree3 -8.00 0.000 0.0000 0.000
## degree4 -10.00 0.000 0.0000 0.000
## degree5 -14.00 0.000 0.0000 0.000
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 8524 8626 8670 8718 8813
## nodematch.X1.F 1918 1967 1992 2015 2054
## nodematch.X1.M 1965 2014 2037 2060 2097
## nodematch.X1.Unknown 45 51 54 56 61
## nodematch.X0 1050 1070 1082 1095 1120
## absdiff.Age 19718 20011 20151 20310 20589
## degree1 -6 -6 -6 -6 -6
## degree2 -10 -10 -10 -10 -10
## degree3 -8 -8 -8 -8 -8
## degree4 -10 -10 -10 -10 -10
## degree5 -14 -14 -14 -14 -14
##
##
## Sample statistics cross-correlations:
## edges nodematch.X1.F nodematch.X1.M
## edges 1.0000000 0.506013821 0.50352757
## nodematch.X1.F 0.5060138 1.000000000 0.01715936
## nodematch.X1.M 0.5035276 0.017159359 1.00000000
## nodematch.X1.Unknown 0.0521729 -0.002297513 0.03169561
## nodematch.X0 0.2109071 0.073681715 0.16862869
## absdiff.Age 0.7277478 0.337087535 0.23001722
## degree1 NA NA NA
## degree2 NA NA NA
## degree3 NA NA NA
## degree4 NA NA NA
## degree5 NA NA NA
## nodematch.X1.Unknown nodematch.X0 absdiff.Age degree1
## edges 0.052172899 0.21090710 0.72774784 NA
## nodematch.X1.F -0.002297513 0.07368172 0.33708753 NA
## nodematch.X1.M 0.031695606 0.16862869 0.23001722 NA
## nodematch.X1.Unknown 1.000000000 0.03852014 0.09121932 NA
## nodematch.X0 0.038520143 1.00000000 -0.01723911 NA
## absdiff.Age 0.091219319 -0.01723911 1.00000000 NA
## degree1 NA NA NA 1
## degree2 NA NA NA NA
## degree3 NA NA NA NA
## degree4 NA NA NA NA
## degree5 NA NA NA NA
## degree2 degree3 degree4 degree5
## edges NA NA NA NA
## nodematch.X1.F NA NA NA NA
## nodematch.X1.M NA NA NA NA
## nodematch.X1.Unknown NA NA NA NA
## nodematch.X0 NA NA NA NA
## absdiff.Age NA NA NA NA
## degree1 NA NA NA NA
## degree2 1 NA NA NA
## degree3 NA 1 NA NA
## degree4 NA NA 1 NA
## degree5 NA NA NA 1
##
## Sample statistics auto-correlation:
## Chain 1
## edges nodematch.X1.F nodematch.X1.M nodematch.X1.Unknown
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 5000 0.7516683 0.7422407 0.7609935 0.8267206
## Lag 10000 0.5801770 0.5547542 0.5915540 0.6732658
## Lag 15000 0.4603087 0.4180819 0.4811029 0.5453079
## Lag 20000 0.3534212 0.3060658 0.3883866 0.4302482
## Lag 25000 0.2528577 0.2418055 0.3192034 0.3312220
## nodematch.X0 absdiff.Age degree1 degree2 degree3 degree4 degree5
## Lag 0 1.0000000 1.0000000 NaN NaN NaN NaN NaN
## Lag 5000 0.8887010 0.8109793 NaN NaN NaN NaN NaN
## Lag 10000 0.7866424 0.6571145 NaN NaN NaN NaN NaN
## Lag 15000 0.7021136 0.5371072 NaN NaN NaN NaN NaN
## Lag 20000 0.6355066 0.4372619 NaN NaN NaN NaN NaN
## Lag 25000 0.5818446 0.3511194 NaN NaN NaN NaN NaN
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges nodematch.X1.F nodematch.X1.M
## 1.5226 0.3117 2.5783
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 1.1857 0.4955 0.9459
## degree1 degree2 degree3
## NaN NaN NaN
## degree4 degree5
## NaN NaN
##
## Individual P-values (lower = worse):
## edges nodematch.X1.F nodematch.X1.M
## 0.127862755 0.755244733 0.009928507
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 0.235735400 0.620244055 0.344178144
## degree1 degree2 degree3
## NaN NaN NaN
## degree4 degree5
## NaN NaN
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).
### Model 7 Still the model does not perform well with updated degree
##
## ==========================
## Summary of model fit
## ==========================
##
## Formula: ga_2.net ~ edges + nodematch("X1", diff = T) + nodematch("X0") +
## absdiff("Age") + degree(1:3) + gwesp(0.25, fixed = T)
##
## Iterations: 20 out of 20
##
## Monte Carlo MLE Results:
## Estimate Std. Error MCMC % p-value
## edges 100.92368 0.76745 0 <1e-04 ***
## nodematch.X1.F -14.39717 0.47522 2 <1e-04 ***
## nodematch.X1.M -9.95276 0.28433 4 <1e-04 ***
## nodematch.X1.Unknown 10.45895 5.90279 1 0.0764 .
## nodematch.X0 0.07386 0.21593 3 0.7323
## absdiff.Age -30.10102 0.16209 3 <1e-04 ***
## degree1 293.97616 2.58069 2 <1e-04 ***
## degree2 190.52786 2.44390 2 <1e-04 ***
## degree3 78.92477 7.25561 0 <1e-04 ***
## gwesp.fixed.0.25 1.37738 0.55530 0 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 38116 on 27495 degrees of freedom
## Residual Deviance: 749561 on 27485 degrees of freedom
##
## AIC: 749581 BIC: 749663 (Smaller is better.)## Sample statistics summary:
##
## Iterations = 16384:1063936
## Thinning interval = 1024
## Number of chains = 1
## Sample size per chain = 1024
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## edges 1592.296 251.9596 7.873739 1.950e+02
## nodematch.X1.F -279.420 23.3252 0.728912 1.709e+01
## nodematch.X1.M 1660.910 6.0511 0.189096 1.916e+00
## nodematch.X1.Unknown -2.952 0.2435 0.007609 5.940e-02
## nodematch.X0 -475.146 44.7189 1.397465 3.030e+01
## absdiff.Age 2886.300 342.8155 10.712983 2.699e+02
## degree1 92.493 2.2645 0.070766 1.592e-01
## degree2 47.561 4.2033 0.131354 2.025e+00
## degree3 -4.979 0.1451 0.004533 5.369e-03
## gwesp.fixed.0.25 2018.375 325.7808 10.180649 2.513e+02
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## edges 1223 1406 1561 1797 2095.3
## nodematch.X1.F -310 -297 -285 -265 -231.0
## nodematch.X1.M 1649 1656 1662 1666 1671.0
## nodematch.X1.Unknown -3 -3 -3 -3 -2.0
## nodematch.X0 -551 -505 -469 -444 -387.6
## absdiff.Age 2383 2634 2852 3172 3567.4
## degree1 89 91 92 94 97.0
## degree2 40 44 48 51 55.0
## degree3 -5 -5 -5 -5 -5.0
## gwesp.fixed.0.25 1541 1775 1977 2283 2669.9
##
##
## Sample statistics cross-correlations:
## edges nodematch.X1.F nodematch.X1.M
## edges 1.00000000 0.99132684 -0.12526221
## nodematch.X1.F 0.99132684 1.00000000 -0.12641307
## nodematch.X1.M -0.12526221 -0.12641307 1.00000000
## nodematch.X1.Unknown 0.39885819 0.42486353 0.23910165
## nodematch.X0 0.98567530 0.96829408 -0.17575053
## absdiff.Age 0.99919003 0.98935111 -0.10005555
## degree1 -0.10033683 -0.09397505 0.01400860
## degree2 -0.83621179 -0.83215863 0.12988549
## degree3 0.02143553 0.03358081 -0.02118473
## gwesp.fixed.0.25 0.99998252 0.99131560 -0.12570837
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## edges 0.39885819 0.98567530 0.99919003
## nodematch.X1.F 0.42486353 0.96829408 0.98935111
## nodematch.X1.M 0.23910165 -0.17575053 -0.10005555
## nodematch.X1.Unknown 1.00000000 0.40156260 0.39339896
## nodematch.X0 0.40156260 1.00000000 0.98143866
## absdiff.Age 0.39339896 0.98143866 1.00000000
## degree1 -0.05702137 -0.09497544 -0.09039615
## degree2 -0.29938302 -0.83003889 -0.83923287
## degree3 -0.02913327 0.01103371 0.02204290
## gwesp.fixed.0.25 0.39884983 0.98571721 0.99913458
## degree1 degree2 degree3 gwesp.fixed.0.25
## edges -0.10033683 -0.83621179 0.02143553 0.9999825
## nodematch.X1.F -0.09397505 -0.83215863 0.03358081 0.9913156
## nodematch.X1.M 0.01400860 0.12988549 -0.02118473 -0.1257084
## nodematch.X1.Unknown -0.05702137 -0.29938302 -0.02913327 0.3988498
## nodematch.X0 -0.09497544 -0.83003889 0.01103371 0.9857172
## absdiff.Age -0.09039615 -0.83923287 0.02204290 0.9991346
## degree1 1.00000000 -0.44879370 0.04805910 -0.1022904
## degree2 -0.44879370 1.00000000 -0.07427729 -0.8351722
## degree3 0.04805910 -0.07427729 1.00000000 0.0215547
## gwesp.fixed.0.25 -0.10229039 -0.83517222 0.02155470 1.0000000
##
## Sample statistics auto-correlation:
## Chain 1
## edges nodematch.X1.F nodematch.X1.M nodematch.X1.Unknown
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000
## Lag 1024 0.9967397 0.9963635 0.9806860 0.9520802
## Lag 2048 0.9934831 0.9927468 0.9608453 0.9041605
## Lag 3072 0.9902240 0.9891875 0.9416382 0.8562407
## Lag 4096 0.9869741 0.9856516 0.9214165 0.8083209
## Lag 5120 0.9836984 0.9820377 0.9025006 0.7604012
## nodematch.X0 absdiff.Age degree1 degree2 degree3
## Lag 0 1.0000000 1.0000000 1.0000000 1.0000000 1.00000000
## Lag 1024 0.9957502 0.9968509 0.6612215 0.8981141 0.25673777
## Lag 2048 0.9915909 0.9936874 0.4575008 0.8353756 -0.02199897
## Lag 3072 0.9874383 0.9904848 0.3161060 0.7912070 -0.02202041
## Lag 4096 0.9832946 0.9872869 0.1794769 0.7482556 -0.02204185
## Lag 5120 0.9790890 0.9840394 0.1266253 0.7300598 0.02438925
## gwesp.fixed.0.25
## Lag 0 1.0000000
## Lag 1024 0.9967200
## Lag 2048 0.9934507
## Lag 3072 0.9901912
## Lag 4096 0.9869426
## Lag 5120 0.9836766
##
## Sample statistics burn-in diagnostic (Geweke):
## Chain 1
##
## Fraction in 1st window = 0.1
## Fraction in 2nd window = 0.5
##
## edges nodematch.X1.F nodematch.X1.M
## -4.2059 -3.7005 1.2851
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## -0.8431 -6.4607 -3.9156
## degree1 degree2 degree3
## 2.1624 8.9570 -0.4088
## gwesp.fixed.0.25
## -4.2399
##
## Individual P-values (lower = worse):
## edges nodematch.X1.F nodematch.X1.M
## 2.600980e-05 2.152092e-04 1.987610e-01
## nodematch.X1.Unknown nodematch.X0 absdiff.Age
## 3.991559e-01 1.042219e-10 9.019679e-05
## degree1 degree2 degree3
## 3.058421e-02 3.336467e-19 6.826770e-01
## gwesp.fixed.0.25
## 2.236109e-05
## Joint P-value (lower = worse): 0 .
##
## MCMC diagnostics shown here are from the last round of simulation, prior to computation of final parameter estimates. Because the final estimates are refinements of those used for this simulation run, these diagnostics may understate model performance. To directly assess the performance of the final model on in-model statistics, please use the GOF command: gof(ergmFitObject, GOF=~model).CUG test
High Assortativity on both Grade and Gender attributes. The Grade has higher assortativity so the assortativity is higher than random generated graphs.
## [1] 0.8271385## [1] 0.9335869
##
## Univariate Conditional Uniform Graph Test
##
## Conditioning Method: edges
## Graph Type:
## Diagonal Used: FALSE
## Replications: 1000
##
## Observed Value: 0.8271385
## Pr(X>=Obs): 0
## Pr(X<=Obs): 1
##
## Univariate Conditional Uniform Graph Test
##
## Conditioning Method: edges
## Graph Type:
## Diagonal Used: FALSE
## Replications: 1000
##
## Observed Value: 0.9335869
## Pr(X>=Obs): 0
## Pr(X<=Obs): 1QAP test
Assortativity test passes for QAP test also. High Assotativity for Grade than Gender. The nodes were not randomly assortative. 
##
## QAP Test Results
##
## Estimated p-values:
## p(f(perm) >= f(d)): 0
## p(f(perm) <= f(d)): 1
##
## Test Diagnostics:
## Test Value (f(d)): 0.8271385
## Replications: 1000
## Distribution Summary:
## Min: -0.1089685
## 1stQ: -0.02563496
## Med: -0.006615038
## Mean: -0.005426089
## 3rdQ: 0.01289734
## Max: 0.1062484
##
## QAP Test Results
##
## Estimated p-values:
## p(f(perm) >= f(d)): 0
## p(f(perm) <= f(d)): 1
##
## Test Diagnostics:
## Test Value (f(d)): 0.9335869
## Replications: 1000
## Distribution Summary:
## Min: -0.08849596
## 1stQ: -0.02509786
## Med: -0.004233134
## Mean: -0.004648804
## 3rdQ: 0.01395662
## Max: 0.1220312Conditional Probability For Grade Match, Male-Male, Female-Female, Male-Female Edges forming
Highest probability for Same grade nodes to form an edge
## Case edges nodemixFF nodemixFM nodemixMM nodematch.XO logodds
## 1 F-M 1 0 1 0 0 -4.7341445
## 2 F-F 1 1 0 0 0 -4.1174639
## 3 M-M 1 0 0 1 0 -3.9536443
## 4 Grade-Match 1 0 0 0 1 0.2547093
## cond_prob
## 1 0.008713375
## 2 0.016024789
## 3 0.018823536
## 4 0.563335289